How to systematically approach truth - Bayes' rule
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- čas přidán 2. 06. 2024
- The philosopher Gottfried Wilhelm Leibniz had a dream. He hoped that progress in philosophy and mathematics would eventually yield a method to systematically figure out the truth. This video explores an approach to that dream that takes us some of the way there: Bayesianism. The basic idea of Bayesianism is to represent beliefs as probabilities and update them using the formal rules of probability theory to the best of our ability. In particular, Bayes' rule tells us how to update our degree of belief in a hypothesis after observing some evidence. Bayes' rule can inform many central tenets of scientific reasoning. One example is Cromwell's rule, which tells us with the language of probability theory that our empirical beliefs shouldn't be absolute dogmas, but always potentially put into question when new evidence comes in.
ERRATA:
- At 8:37, there should be P(H|e) on the left-hand side.
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Arbital's guide to Bayes' rule: arbital.com/p/bayes_rule/?l=1zq
The bayesian view of scientific virtues: arbital.com/p/bayes_science_v...
@3blue1brown 's explanations:
1. • Bayes theorem, the geo...
2. • The quick proof of Bay...
3. • The medical test parad...
4. • Why “probability of 0”...
5. • Binomial distributions...
@measureofdoubt's explanation of bayesian thinking: • A visual guide to Baye...
Two beautiful books containing many essays on bayesian thinking and truth-seeking:
1. Map and Territory, by Eliezer Yudkowsky: www.amazon.com/Map-Territory-...
2. How to Actually Change Your Mind, by Eliezer Yudkowsky: www.amazon.com/Actually-Chang...
Probability Theory, The Logic of Science, by E.T.Jaynes. This is THE book on bayesian thinking applied to science (more advanced):
www.amazon.com/Probability-Th...
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Script by:
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- The guy with the weird accent
Animation by:
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Narration by Robert Miles: / robertmilesai
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▀▀▀▀▀▀▀CHAPTERS▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
Chapters:
0:00 - Mathematicizing truth-seeking
1:55 - Conditional probability
3:39 - Explanation of Bayes' rule
10:34 - The odds form
14:54 - Cromwell's rule
17:36 - The bayesian view of truth-seeking - Věda a technologie
Many of our future videos will probably be more comprehensible if you understand Bayes’ theorem and assimilate Bayesian thinking. If you found the grabby aliens’ videos somewhat confusing, try to go back to them after having understood this one! The video about prediction markets also shares the same approach of attaching probabilities to beliefs.
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Amazing channel. Beautiful animations and great explanations.
How the heck does your video have so few views!?
Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.
John 14:6
Selah
@@SeektheLordsface Ok, I'll bite. Let's think about Jesus using Bayesian probability. The observed likelihood of people coming back to life after dying is pretty tiny since there are no agreed upon/verified examples. The number of people who have been observed and verified to stay dead after dying is easily in the millions as a lower bound, although plausibly you could use a number of billions since it doesn't seem like anyone has physically come back to life in the last few centuries and billions have died in that time span.
This gives us somewhere in the 1/million to 1/10 billion range for the prior probability of Jesus coming back to life after dying, regardless of whether a God exists since that God evidently usually doesn't raise people back to life. What evidence is cumulatively strong enough to give better than 1 million times stronger support (likelihood ratio) to the hypothesis that Jesus truly rose compared to alternative hypotheses like a couple of the disciples lied or had grief hallucinations that moved the other disciples to true belief in his resurrection?
@@davidlovesyeshua what year is it and why?
What do you mean God doesn't raise people from the dead? How did you get to that conclusion from someone who obviously doesn't want anything to do with God?
I learnt Bayes theorem 3 years ago, understood 2 years ago, forgot 1 year ago, again understood this year when CZcams suggested me this video .❤
"the maths of truth-seeking" is a bit more polite than the one I heard in college stats class; the one I heard was "statistics is the mathematical theory of ignorance"
Physics is rigorous truth seeking
Lol, someone using statistics who doesn't understand statistics is one of the most frustrating things imaginable. You don't get to stop at the result you want, you have to keep going until you reach the highest possible statistic so you have context. Then repeat that with several independent data sets. Then you need to actually investigate because correlation isn't causation. So much easier to generalize 😑
@@Zarkil "It either is or isn't, so everything is a 50/50 chance"
Statistic is a great way to deceive peoples without straight up lying to them. Just present the results the way you want.
Anyway here is a joke : Two statisticians go hunting, they see a bird. The first one shoot, too far to the left. The second one shoot, too far to the right. One look at the other and says : "in average we got it".
@@techwizsmith7963 thats not how it works
Favorite channel by far, thanks to your Grabby aliens video I chose to major in statistics. My probability classes are probably my favorite
What is the probability that statistics is probably your favorite class?
Dude, you are one of the special people we need in this world. Everything here is beyond my stoned mind.
this is the next kursgesagt, I can already tell...
Bayes' rule saved so many peoples. Knowing the ods of false positive is really important in medecine.
Everyone should always get a second test performed. Even by the same doctor and same lab, on the same day. Two positives really narrows down the fact you actually have X.
Thank you for this video. Very timely, as I've been dipping into the literature on truth and rationality. Never read Bayes, or Bayesian reasoning. Thanks for the video.
If you want to go further, there's plenty more material linked in the video description!
It’s super useful in evaluating truth claims. It’s like a bullshit detector.
@@moonandstars1677 have you actually used it?
@@quentinortiz4837 have you?
@@AJ.Rafael no, but I did asked my statistics teacher about it. He criticizes it for being too simple and not that reliable as some people hold it up to be
This is SUCH A GOOD VIDEO! I had a hard time fully grasping the whys of Bayesian statistics but now it makes a lot of sense!
The most accessible explanation of Bayesian thinking that I’ve encountered so far! ✨Thank you so much for creating this video! 🙏😊
I second that emotion. Bravo!
@@tanyavisceglia6160 I also agree
I'd say 3blue1brown is just as or even a tad bit more intuitive, although this channel was the most entertaining. Good thing we can watch/link both! :)
An exception to the 'never say 100% or 0%' is the rule itself, which should be applied in 100% of cases. :)
no. not even this can be applied in 100% of cases. Consider black holes. What is the probability that you will fall in it, if you reach event horizon?
@@anonimanonim2710There is always some low probability that the laws of physics we know are wrong.
"The rule 'no 100% or 0%' is always useful on practice" shouldn't have 100% probability. So, the statement applies to itself quite fine.
@@pavelgorokhov2976 the probability is 100%, because the gravity there is so strong it affects time. So falling in it becomes a sort of destiny, rather than a destination
@@anonimanonim2710 there is an incredibly minute possibility that for some reason we are wrong about everything due to some factor that just so happened to make the laws of the universe look exactly as they would look if our models of the universe were false. that chance is incredibly small, but it isn't zero
This is a FANTASTIC video on intuitive understand on Bayes. Loved the animations. Loved that you explained the odds for of Bayesian. Loved the examples.
Always excited to see a new video from y’all pop up in my feed!
Wakes up at the sound of someone at the door :grabs the calculator:
I find it astonishing that I don't remember ever hearing about Bayes rule until now, but despite that fact. This is precisey the way I tend to think about beleifs.
I probably simply absorbed this way of thinking through being an avid follower of various science topics, and classes that taught the scientific method without ever directly referencing Bayes.
I appreciate that sam o'nella music in the background, excellent subject and video. Criminally underrated.
Thank you for taking the time to gift us with your amazing thought process!
Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.
John 14:6
Absolutely amazing video!
These videos strive for clarity in a refreshing way
Definitely the best video I've seen on Bayes' rule. This really helped me understabd it better, snd i loved the animations!
always love a new video from this channel!!
i have watched tons of videos but none of them explain this much good , you are the best
Nice, integrating a statistical formula into everyday thinking so that our reasoning is more objective.
Superbly clear AND memorable because of the greatly entertaining presentation!👍👍👍👍👍
This is a great video, and I should really watch it a few more times.
Probably the best video I’ve seen on Bayes rule! Good job
It is
It is
Really love this content as someone who took stats and has heard of Bayesian epistemology but never really delved into it :D
I'm sure the Bayesian community has already addressed this, but I think I would recommend at least one alteration to the rule of excluding one and zero from your set of probabilities. I think that either tautologies and contradictions should be excluded from the domain of your probability functions or your probability function should have the property that 0 is assigned to and only to contradictions and that 1 is assigned to and only to tautologies. The first option would definitely be better.
I disagree with this. I'm not sure how to elaborate, sorry.
A common view is that you can never be 100% sure that a statement is a tautology/contradiction. While your analysis may say that something is definitely a contradiction/tautology and therefore false, the probability you give it should never be 0 or 1 because your analysis is not perfect. The result may seem counter-intuitive but everyone makes mistakes in reasoning. Consider this, can you correctly identify a contradiction EVERY TIME when given 5000 contradictory and 5000 non-contradictory statements? It seems to me that almost everyone will make at least one mistake. Even if we say that some people are just so good at logic and they will never make any mistake in a task like this, someone being one of those people will never be 100% certain. So in that case as well we cannot (should not) assign probabilities of 1 or 0 to statements.
Another reason to not give them probabilities of "0 or 1" is that once you have done that, mathematically, you can never be convinced otherwise. If you incorrectly called something a contradiction and gave it a probability of 0, nothing should ever be able to change your mind since 0 times anything is 0. Same for giving something a possibility of 1. Once you made an incorrect call game is over and we will make incorrect calls because of the reasons I articulated above.
@@HuseyinOmerErgen Thank you. Real things have logical uncertainty.
@@HuseyinOmerErgen This is the correct analysis. To make it a bit more obvious, you can consider the possibility that your brain is struck by cosmic rays in just the right way at just the right time to cause you to misidentify a tautology, even if under normal circumstances you think you ought to be incapable of making a mistake on something that easy to identify. Or if cosmic rays aren't enough, some undiscovered property of dark matter/energy, a side effect of advanced alien tech probing your mind, cartesian demons, etc.
There's just no practical use or philosophical justification for probabilities of 1/0 when we can just say "for all practical purposes this is effectively certain even though it technically isn't" and move on.
Although that does actually make me think of 1 motivation for 1/0 probabilities and that's use in mathematical models, but that's easily solved by distinguishing between in-model and out-model confidence. I can make a model, plug numbers in such that something has a probability of 1, and then simply assign less than 100% credence to the model itself being accurate.
@@davidlovesyeshua Yeah definitely. I subtly acknowledged the inside-the-model & outside-the-model epistemic difference by the phrasing "While your analysis may say that something is definitely a contradiction..."
Love your animations. Amazing work!!
A very good explanation of Bayes' rule. Thank you.
This has a beatiful animation, you deserve way more views, thank you for this video
Great video!! If I ever mention Bayesianism on my channel, I'll refer to this video. Loved the animations and how well they fit the script.
- Jeroen
Thanks for this explanation. I've heard of Bayesian formula but I've never understood it's odds formula until now. BTW, I would like to suggest you tackle fuzzy logic. I believe it can have practical applications.
This channel reminds of Kurgestat in a nutshell and I love it. Keep up the animations.
really great explanation
Excellent presentation
This video gives me this chills.
at the end Im glad you answered what I was going to object with which was going to be "Yeah but how do we apply this to things we cant pin point an exact number for our confidence level?"
Very nice video. Thank you!
Excellent video yet again
Only 80.000 views, that is kinda disappointing.
This video was very nice animated and clearly explained.
Thank you for also introducing the historical aspects and the idea of Bayesianism instead of just showing the formula and explaining the individual parts that most of the people do.
By introducing more about the context and background it helped understanding the content of the video.
This makes a lot of sense, compare to the alternative, judge based on all possibilities.
Stats is very practical.
very interesting and useful
I love your videos! Could you record 20% louder, please. I'm not very deaf, but this one is much quieter than other CZcams content. Thanks
Love the animation with chill cat and doggo 🪄
Important video. Delusions or those otherwise hopelessly biased in their beliefs are not amenable to Bayesian persuasion, for example.
@14:10 fun fact... that's why home alarms here don't send someone for every alarm. They only call emergency services if at least two separate systems go off. If the window reports as broken and there is someone in the kitchen for example.
Great Video!
Great video! 👍
Awesome, thank you
I have had this type of thinking for nearly half my life now. In common English I will say that I believe things that I have more than two deviations of certainty.
15:14 Here's one possible exception I found (Spoiler if you want to figure it out yourself)
The probability that I exist at the exact moment I am thinking this thought is 1, and the probability that I do not exist at the exact moment I am thinking this thought is 0.
Then there is the "Mind in the Jar" hypothesis, which can indicate that the probability of you not existing at that spot, at the exact moment you're thinking, to be more than 0 (around 1: 1 trillion and less, but still)
What if it's all a simulation though?
**Nick Bostrom checkmating Rene Descartes**
None of the two replys above me matter though. The exception is about existing. Whether one lives in a simulation or in reality or in a jar doesn't matter to the question whether one exists in the first place.
You could only *think* you were thinking this thought, but really only have false memory of it.
"exact moment" is a mental construct anyways.
@@musaran2 I'm confused what you mean, the exception he gives isn't about what he thought in the past, it's about the present. If you want to try the exception out for yourself, just think to yourself "I exist right now with probability 1"
Amazing videos . Which softwares do you use to make such outstanding videos ?
So sad that this video has so few views despite it having the biggest impact on someone once they understand it.
Unfortunately I think the people who would benefit most from this are also the people least likely to understand what it actually means.
@@Zarkil Yvain's essay "Should You Reverse Any Advice You Hear?" seems relevant.
Wonderful! Easy to follow explanations, good narration, the animation both helped me understand what was being explained and was also adorable, I loved it!
As someone who has shyed away from diggin deeper into Bayes so far, I really appreciate this video!
Good narration??? Monotonous, without punctuation...seems like one 19 minutes long sentence. It is obvious that it is being read without caring about the listener.
Sorry for harsh critic, but this is a chance to improve.
Please spend some time watching channel Veritasium and see what is good narration.
@@occamrazor5180 I like the narration. It's calm, sure, but I wouldn't call it "monotonous". It uses emphasis to help you better understand what is being said, not for show.
Have you tried turning on subtitles? They're well done and might help you follow the explanations better.
@@cptn.penguin902 Was this a jab? :) I understood everything, I mean till the point I listened. Honestly I'm not expecting Laurence Olivier in Hamlet...This was relentless declamation. We might not agree, but I'm right 😉
@@occamrazor5180 I'm sorry if what I said came of as a "jab". I was genuinely trying to be helpful. Audio processing issues are pretty common, after all. I always use subtitles, if they're any good.
And if you simply don't like the video, that's fine, too.
@@cptn.penguin902 I apologise to you. I was simply a little bit frustrated that what was a promising video wasn't up to my liking. Well, to each his own. Thank you for civil conversation, and I again apologise for harshness.
I want that logo as a plushy :)
I literally just cant follow up... I always wanted to understand what is being explained in this video because that's the most important basic method of thinking humans came up with to maximize our own overall "success" in our environment.
But i literally can't... I always lose track because it's too much information and i cant put too much information "on hold" when i need to in order to solve an emergent problem... then i have to go back, and make a huuge mental effort to recap and understand whatever information i couldnt understand that made me lose track.
I have severe ADHD so i have VERY LOW mental energy to do this EXACT type of process thinking.. i literally can't keep trying for more than 5 to 10 minutes... I start to feel mental exhaustion and something that resembles physical pain, but it's not. It's hard to find the correct words.
After trying and feeling like that a few times i literally quit trying even having the desire to understand what i gave up understanding.
School was HELL for me.
I feel you, adhd brain here as well. What I noticed though, for some problems my brain actually requires way more information than I think to make a decision. You need a certain threshold of input information to synthesize it into a new pattern. Basically the way you need a certain amount of whatever for emergence to do its thing and turn quantity into quality. And the more diverse information the better.
Not every decision needs to be taken this way (in math equations) and I like that one doesn't need to know super advance math to understand how it works and apply it, just logic!
I find it helpful to write it all on paper so it doesn't tax my working memory until I have zero WM left (I assume you are also lacking in it since you have severe ADHD and that is probably an important cause of your problems). Then I play around with things (again) by writing on paper until things start to feel intuitive enough and I don't need to keep things in my working memory.
Have you tried medication?
Perfection!
I'm honestly shocked that this isn't more wide spread, at least not that I've noticed. While I doubt it (or anything truely) could have been a cure all, it genuinely feels like it could have lept us forward in how we approach the world as a whole. The best part of this is that it can challenge itself. Set H as the possibility of it working out for the better of the majority with e being the evidence. Since from what I understood, you start with H first before looking at the evidence and it would be harder to set than your examples. If I had to, I would use what would make the most sense from what I understand of Bayesianism and what I can reasonably conclude about it. Then I go into the evidence to adjust my probability and thus by its own rules, we can determine its effectiveness and how confident in its method.
There are probably some errors in this as I am just learning about Bayesianism from this very video, but I hope I got my point across. Heck you could probably make that into a Baye's equation. To me at least, a formula that can challenge itself with its own rules is HUGE, doubly so as it asks us to never be 100% or 0% sure about anything. Like you said with the moon being made of green cheese, it can prepare us for when that 2% ends up being reality. It would be like the difference between a bridge suddenly but slowly collasping to a bridge just suddently dissappearing from under out feet (paws). Sure, neither are ideal, but one gives us more time to react to safety than simply dropping us toa our doom, hopping for that 1% chance of surviving that fall becomes reality.
Thank you so much for sharing this with us!
criminally underrated
Very good animation 🫶🏻😊
I saw the Chill Cat! I have blurry, not-made-up pictures!
Pretty cool dude.
The Crestus app by Richard Carrier has a really good Bayesian calculator on it though I imagine there are apps dedicated solely to that if y’all wanna play around with it.
More comments for the algorithm! So many people need to see this video, just look at the whole pandemic and all those who reject science
Really wondering how the illustration humor is both conceived of by the artist and/or writer, and how it's so well coordinated to be so deliberately integrated with the narration side of the video, whilst remaining so consistently cute..
Do you have help from AI?
You should do a video about Chris Langan’s CTMU
Would we have the minds to follow through on the calculations even if known. Im doubtful
I would be overjoyed if I was the 4th view on this video and then it got taken down for copyright reasons.
Nice
Bayesian Statistics is very interesting, yet very tricky
What is the backround music called? I recognize it from Sam O' Nella's vids
0:50
"This video will reach 1 million views within a year P~10%"
Coincidence: Eliezer Yudkowsky claims he would've said 10%, if someone had asked him how likely HPMoR was to become at least as popular as it eventually did.
Positing that it and YT stands;
The probability this video will be kissed by the algorithm and recommend it to absolutely everyone randomly 3-15 years from today... 100%. No equation needed.
It's amazing seeing rationalist videos of this quality! But I'm disappointed you so quickly dismissed the chill cat!
It's been 4 months, will you ever upload again?:o
I saved lots of money on burglar alarm. Thanks!
I just wanted to show my suppurt for my team...
In real life there are a tiny fraction of beliefs for which the required probabilities to complete these calculations are knowable, and of those a similarly tiny fraction are known. The vast majority would require estimates which are largely subjective. So the true value of the formula is not in broad applicability of the actual calculations, but as a means of understanding the sorts of information we should consider in making rational decisions, and how that information interrelates.
Bayes' rule is very useful in the field of history, but unfortunately it's not very accepted among historians. Perhaps in the future it will be.
It’s useful in gambling and investigating crimes too
What if your probabilities are measured by qbits? By reducing every probability in the system to a comprehensive system of Booleans, a quantum computer should be able to produce a set of solutions. Consequently, measuring the number of each type of outcome against the total number of measured solutions would result in the probability that scenario would occur (I assume). Would this theoretically achieve the same result as the Bayesian calculations? Would it be more or less accurate? And can we even practically expand an arbitrary probability function into Boolean cases without accounting for every quantum measurement for every particle in the system in the first place?
I wonder if a neural network could arrange such a complex Boolean directed graph from a description of the evidence and postulation… 🤔
In my opinion (strong emphasis on opinion) the benefit of this equation isn't the answer you get, it's the way you have to think to work the problem. It's an equation that teaches unbiased critical thinking.
what if I know that my friend gets sick but never complains? What if I don't know if my friend ever gets sick because he never complains, but I know that I don't complain even when I get sick?
Information exists is shown by every form of evidence, whether it be empirical/induction, synthetic/deductive, apiori, posteriori, etc, so in a way it has infinite evidence just by evidence existing because alternatively nothing exists which is a self contradiction. Which leads to my question of doesn't some mathatical proofs count as infinite evidence like proof by contradiction or no because their deduction is based on axioms that you would say we should have some doubt because they are assumptions?
love the sam o nella music in the backgrounds
What's the source for dannis victor lindley saying you should always consider the hypothesis that the moon is made of blue cheese? Google doesn't return any results...
Chillcat sounds like a parallel universe version of updog.
Math is hard but cute doggy make it easier.
Conditional probability to me has a lot in common with Quantum math , namely that I can stare slack jawed at it and listen to explanations all day long and nothing ever sticks. And this despite my being quite comfortable with some damned abstract math concepts like Group Theory, Category Theory (abstract algebra in general), GR, Calculus, Algebraic Geometry, Topology, etc.
I can grok that conditional probability and bracket notation are actually incredibly simple in and of themselves. Shockingly few moving parts, on a par with ordinary ratios.
But I still look at them and feel like Meatwad from Aqua Team Hunger Force floating about in the ocean saying "Do what now?". :(
A fair coin does not have a 50/50 chance of landing on a particular side. Coins have an edge which is a factor. Though it's essentially negligible it still has an effect on the outcome. And there have been time when coins land on their edge, I've seen it
1 thousandth like 🥳🥳🥳
I have a headache after watching this video. What are the probabilities of that? 🤔😵💫
why do we need to multiply two probabilities ?
the percentage of video that has shibe on screen approaches 100%. the future is bright
Isn’t there an error at 8:37? Shouldn’t be P(H|e) on the left-hand side?
You're correct. I'm adding an erratum in the description.
@@RationalAnimations pay attention because I spotted other typos here and there. However, it is a nice video, good job 😊
Id like to meet the chill cat, can you give us more info on the chill cat please?
My brain is too small for this.
Me too but I watch because doggo is cute
There must be something missing in the formula, something that assigns value or importance to the hypothesis. So in the burglary alarm example, having someone breaking into your house has a higher importance than a false alarm, lending it more credence. More so if your house had been robbed before and the experience was traumatic. To treat every alarm as true until proven false seems perfectly reasonable to me, and it is in fact how most public places behave.
Giving value to the hypothesis would explain a lot of what we perceive as irrational behavior. That is, it could change our opinion of a person's thoughts or behaviors, and perhaps allow a more rational, productive discussion about it.
That's risk assessment, not likelihood assessment.
Something can be unlikely but still worth protecting against in the case that it occurs anyway.
About the 0% /100% stuff:
I think the exceptions where you can be 100% certain are tautologies (stuff that can:t be false for purely logical reasons) and subjective experience as such (not "things are as we recognise them", but rather "I'm currently having some kind of subjective experience")
The charitable interpretation of people saying they're 100% certain is that the difference is small enough so it doesn't matter if you aren't extremly nitpicky (like 99,99999%)
noone: "all humans have 4 legs."
bayesians: "that is highly unlikely!"
@@HUEHUEUHEPony i'm pretty sure that's not the only reason. ;)
Gonk
To increase understanding,
decrease playback speed.
One of my foundations:
I don't believe anything 0% or 100% anymore.
Robert Miles for narration is nice
I wonder if there will ever be people with radical ideas like this now that we live in a world where some things are known to be mathematically impossible to prove, but could be true.
It seems like you would have to ignore that to assume all things can be proven
But incompleteness doesn't stop us from having a rational basis for making everyday decisions!
(And there are some promising workarounds even for Gödel-type limits on mathematical reasoning, like expanding the true-false dichotomy to support self-referential statements like a Gödel sentence.)
The left-hand side of the equation should say P(H|e) at 8:39...8:56
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